U.S. officials and some of their Iraqi comrades in arms were skeptical of an official Iraqi military claim today that it wounded ISIS leader Abu Bakr al-Baghdadi in an airstrike west of the capital, Baghdad, but said his days may be numbered.

American and Iraqi officials contacted by ABC News were in dispute over the strike today, with one Iraqi official claiming al-Baghdadi was in the targeted city of al-Qa'im but most of the others voicing strong skepticism.

Numerous senior American counterterrorism officials made it clear they aren't uncorking Champagne in celebration just yet, though some reiterated that al-Baghdadi is being aggressively hunted amid a stepped-up U.S.-led campaign in Mosul and may not survive for long.

"We don't have any information to corroborate it. Baghdadi is somebody we'd like to see meet his end, but we've not had any info to corroborate," said Capt. Jeff Davis, a Pentagon spokesperson. "It was their strike. They announced it."

ABC News reported on Jan. 20 that senior American military analysts believe that the reclusive al-Baghdadi has been hunkered down in ISIS-occupied Mosul in northern Iraq since Iraqi government forces moved on the city, the country's second largest, last fall and that he has not visited the de facto ISIS capital of Raqqa in Syria in months.

Raqqa is increasingly under pressure by and American-directed coalition of Kurdish and Iraqi forces.

The Iraqi government previously claimed that al-Baghdadi had been wounded or killed, and the latest report centered on a weekend airstrike the Iraqi military said it launched against ISIS leadership in al-Qa'im, a town in the western Iraqi governate of Anbar.

"The Falcons intelligence cell carried out an operation to target ISIS leaders in al-Qa'im after the cell was able to track, through its sources, a convoy that was carrying the terrorist Abu Bakr al-Baghdadi and some other leaders from Syrian territory into Iraqi territory in the Qa'im district," an Iraqi army statement said.

The title of the official statement said al-Baghdadi was injured, but the statement did not provide details beyond claiming that "13 terrorist leaders from ISIS were killed."

One Iraqi intelligence official, who requested anonymity, claimed the Saturday bombing wounded al-Baghdadi while he met with other ISIS commanders in a one-story house.

But other Iraqi intelligence officials told ABC News that al-Qa'im is far outside areas he is known to have visited in the past year, and another said the reports of his being wounded were "lies, part of psychological warfare. Over the past 72 hours there haven't been any such operations by the Iraqi air force."

Several U.S. intelligence agencies declined to make any official comment about the Iraqi military claims.

The Mosul offensive, which has liberated the eastern half of the city this year, is directed by the U.S. military. The U.S. Joint Special Operations Command and sometimes the CIA track targets and direct airstrikes in northern Syria and Iraq aimed at ISIS leadership and al-Qaeda's Syrian affiliate.

Iraqi officials claimed al-Baghdadi was wounded or killed in airstrikes numerous times over the past two years, only to have the self-proclaimed caliph, or leader of all Muslims, issue a statement or audio recording, as he did last fall, rallying followers to defend Mosul, which has been under a U.S.-led siege for months.